This disclosure relates to systems and to methods for analyzing objects that contain a flow field and whose features appear to develop randomly. It relates to systems and to methods for measuring apparent random patterns created in the form of paths and pathways in structures that contain flow fields. In particular, this disclosure relates to systems and to methods for image segmentation of flow systems.
Seemingly or apparent random patterns and pathways are often a part of systems and objects that occur naturally and that generally contain a flow field. An example of a naturally occurring random pathway is a river that travels across the landscape. The river possesses several bends and tributaries and it is often difficult to predict which section of the river will contain a bend or a tributary. Another example of a naturally occurring random pathway is the path taken by blood vessels in the eyeball, the heart, the lungs, the brains, or other parts of a living being. Blood vessels have a number of branches and it is difficult to predict where these branches will occur, the number of branches and the average orientation of these branches that a particular part (e.g., the heart, the eyeball, and the like) of a particular living being will have. A tree is another example of a naturally occurring structure whose branches take random pathways and the point of contact of one branch with another is an apparently random event. All of the aforementioned examples—the river, the blood vessels and the tree contain flow fields.
The ability to determine and to measure the structure of such apparently random objects permits predictive capabilities for the design of future objects. It also permits a comparison of one set of the objects (that are grown or developed under one set of circumstances) with another set of equivalent objects (that are grown or developed under a second set of circumstances). It is therefore desirable to develop methods that can be used to measure the structures and to quantify their features so that they can be compared with one another and to predict the behavior of future objects. It is also desirable to facilitate preservation of network connectivity, improve network connectivity where possible, and correct faulty and erroneous pathways with improved accuracy over current methods found in the literature.